Senate Majority Leader Robert J. Dole (R-Kan.) yesterday challenged the Reagan administration's policy of "constructive engagement" in South Africa, telling White House chief of staff Donald T. Regan that it is "a matter of growing concern in the Congress" and a serious domestic political issue.

Regan vigorously defended the president's policy during a luncheon meeting with Dole at the White House to coordinate legislative strategy when Congress returns from the Independence Day recess next week.

"He Dole said, 'What the hell does constructive engagement mean?' and I said it means that we're not going to turn our back on South Africa, we're going to stay in there and talk to them," Regan said after the meeting. "If we were to pull our ambassador out, put sanctions on them and the like, we're not a player. We have to sit at the table and deal even though we may not like what is happening on the other side of the table."

Dole said "it would be my hope" that the administration would toughen its approach toward South Africa, but Regan said he gave no signal of any policy change. He said he and the Senate majority leader saw eye-to-eye on most issues discussed at the meeting, which also was attended by Regan's top legislative strategist, Dennis Thomas.

The House last month passed legislation calling for total U.S. disinvestment in South Africa, and the Senate Foreign Relations Committee is scheduled to begin hearings on this and other proposals on July 22. Some Republican strategists have advised Regan that South Africa could become a political liability for GOP candidates this fall, according to White House officials.

"I do believe that, in addition to becoming a very serious international problem, this has now become a domestic civil rights issue," Dole said.

He said he made this point to Regan and also questioned whether "constructive engagement" had persuaded the South African government of P.W. Botha to moderate its policies.

"I indicated that we in Congress would like to know what constructive engagement has produced," Dole told reporters. "If that's the policy, what is it, and what has it produced?"

Regan said he suggested that conditions might be even worse in South Africa if the administration had "pulled out" and disputed Dole's view that the policy should be determined by domestic political considerations.

"I said it shouldn't be a domestic issue, anymore than the Irish question or the Polish question," Regan said. "This is definitely a foreign policy issue . . . . We are doing our best to help the blacks in South Africa."

National security affairs adviser John M. Poindexter last month announced a high-level review of U.S. policy toward South Africa, but Secretary of State George P. Shultz said subsequently that this was mostly tactical in nature and would not involve a reconsideration of administration opposition to punitive sanctions.

White House spokesman Larry Speakes said yesterday that State Department recommendations on South Africa are being reviewed by members of the National Security Council staff and Regan, and will be the subject of an NSC meeting.

No decision has been made on whether the president will give a major speech detailing his views on the South African situation, Speakes said.

At their meeting, Dole and Regan agreed that the sluggish economy could boost the federal budget deficit. Dole suggested that some tax increases might be necessary, Regan said, but both men agreed that it would be impossible to consider a second tax bill this year. A House-Senate conference committee will attempt to work out differences between House and Senate versions of major tax-overhaul legislation after Congress returns from its recess.

Dole said he suggested an increase in the federal telephone excise tax as a possible additional revenue source.

President Reagan flew by helicopter to Camp David yesterday and is scheduled to remain there until Sunday afternoon.